Mandel: software for real and complex dynamics

• Draw the Mandelbrot set and Julia sets in two windows at the same time. Available methods of drawing include escape time, hyperbolic components or attracting basins, distance estimate, marking external rays or puzzle-pieces. Display Julia sets on the Riemann sphere.
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• Trace equipotential lines and external rays,
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  in the parameter plane and in the dynamic plane as well.
• Discuss the combinatorics of external angles, kneading sequences, and internal addresses. Illustrate the Spider Algorithm and Thurston Algorithm.
• Find centers and Misiurewicz points in the parameter plane, or periodic and preperiodic points in the dynamic plane.
• Illustrate renormalization by marking small Mandelbrot sets and small Julia sets. Mark
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  embedded Julia sets by a kind of preperiodic renormalization.
• Display the asymptotic self-similarity at Misiurewicz points on multiple scales, and the local similarity to Julia sets.
• Draw the parameter plane and Julia sets for other one-parameter families, which satisfy critical relations or show a persistent Siegel disk. Available are unicritical polynomials, Branner-Fagella polynomials, various families of cubic and quartic polynomials, quadratic rational mappings, Newton's method,
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  transcendental functions, a simulation of quasiconformal surgery, the Tricorn,
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  Henon mappings, and the Barnsley–Bousch–Thurston IFS.
• Compute and display the core entropy and biaccessibility dimension for dyadic angles.
• Save images as PostScript *.eps, save or load a *.png image.
• Animated demos
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  provide an extensive introduction to basic and advanced aspects of complex dynamics.
• Start Mandel from the GAP package IMG by Laurent Bartholdi. E.g., this package can compute a mating from combinatorial data.
• Future plans include the construction of Hubbard trees and incorporating real iteration.
• The program contains a few languages: English, German, Polish (by Adam Majewski), and Portuguese (by Atractor).